Can I upgrade my iMac El Capitan
Upgrade to macOS Sierra or High Sierra?
iMac, OS X 10.11
Sierra has the same iMac requirement as High Sierra
How to upgrade to macOS Sierra - Apple Support
iMac introduced in late 2009 or later
2 replies
If it is in the list of supported Macs in this article:
How to upgrade to macOS High Sierra - Apple Support
So basically:
iMac introduced in late 2009 or later
Good luck!
Can I upgrade my iMac El Capitan